Robust and exploratory analysis of active mesoscale tectonic zones in Japan...

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Tectonophysics 400

Robust and exploratory analysis of active mesoscale tectonic

zones in Japan utilizing the nationwide GPS array

Yuzo ToyaT, Minoru Kasahara

Institute of Seismology and Volcanology, Hokkaido University, N10W8 Sapporo, Hokkaido 060-0810, Japan

Received 5 April 2004; accepted 3 February 2005

Available online 29 March 2005

Abstract

A monitoring GPS array recently developed in Japan can yield nationwide maps of active inland tectonic zones (ATZs) on a

mesoscale, approximately 70 to several hundred kilometers in lateral extent. But it has been difficult to characterize ATZs in

Japan, as they are in fact operational on multiple scales and our efforts are often hindered by various irregularities in the data.

The key to overcoming these problems would be to gain an insight into the available data before any precise kinematic

modeling is performed with indefinite assumptions. In this study, horizontal velocity fields, deduced from the nationwide GPS

array, were treated with a set of techniques in robust smoothing and exploratory data analysis that brought out exceptionally

powerful mesoscale ATZs, and made them easier to characterize. The resolved ATZs were then retrospectively monitored to

study their regional and temporal variations, using a set of approx. 840 observation stations, about 30 km apart, for a 4-year

series of fixed observation time-intervals, 810 days each. The smoothing operation involved three steps: (1) imputation of the

velocity fields for the purpose of anti-aliasing, (2) robust smoothing of the velocity fields with the median operative, and (3)

visualization of deformation-rate distributions in several coordinate independent parameters, and post-filtering. The geometrical

resolvability of mesoscale ATZs was confirmed by calibrating the smoothing scheme against synthetic tectonic boundary

models before it was applied to the case study in Japan. ATZs in Japan, which are essentially visible as systematic deviations in

the velocity fields on the International Terrestrial Reference Frame (ITRF) and as strain rate anomalies, were highlighted sharply

along some known tectonic zones, chains of active volcanoes, and areas above low seismic velocity anomalies in the crust and

upper mantle, all of which generally paralleled the offshore trench axes. The geometrical agreements among the mapped ATZs

and the physical anomalies in the crust are presumably due to their common structural weakness on the mesoscale. In the four

main islands of Japan, all but 30–40% of the strain rate anomalies persisted during the entire 6 years of the case study period,

while the rest sporadically appeared or disappeared in a period from several months to a few years. The transient shifts in the

deformation rates were remarkably synchronous with some nearby major tectonic episodes: large earthquakes and slow events.

Differential plate coupling strengths along the subduction zones can also be inferred from the persistent pattern of rotational

strain rate anomalies forming clockwise and counterclockwise pairs along the Pacific. Our empirical observations suggest that

the first-order features of interseismic crustal deformations in Japan can be characterized as collateral processes behaving in

0040-1951/$ - s

doi:10.1016/j.tec

T CorrespondiE-mail addr

(2005) 27–53

ee front matter D 2005 Elsevier B.V. All rights reserved.

to.2005.02.003

ng author. Tel.: +81 11 706 2643; fax: +81 11 746 7404.

ess: [email protected] (Y. Toya).

Y. Toya, M. Kasahara / Tectonophysics 400 (2005) 27–5328

response to fluctuations of the tectonic stresses on multiple scales, likely influenced by changes of plate coupling strengths on

the contiguous subduction faults.

D 2005 Elsevier B.V. All rights reserved.

Keywords: Active tectonic zones; Crustal deformation; Earthquake; GPS; Japan; Strain rate changes

1. Introduction

Tectonic boundaries are complex (e.g., King,

1983) just as much as hierarchically distributed

tectonic blocks (e.g., Turcotte, 1992). Particularly

as Japan is situated at the confluence of several

major tectonic plates (see the insert in Fig. 1, upper-

left), tectonic block segmentation (e.g., Mogi, 1985;

Tada, 1986) might be prevalent in the area. Between

pairs of major tectonic blocks, there are confined

zones of active tectonics up to a few hundred

kilometers wide (McKenzie and Jackson, 1983) that

often host large inland earthquakes (e.g., Jackson et

al., 1997; Sagiya et al., 2000). A good example of

this is the Niigata–Kobe Tectonic Line (NKTL), a

zone of concentrated deformation that was recently

identified using the nationwide GPS array in Japan

(Sagiya et al., 2000). Still, the geometrical resolution

of the suggested zone is indeterminate, and the

nature of development or the temporal variation of

deformation rates on such zones remains to be

explored. Elucidating the geometry and the charac-

teristics of deformation along dactive tectonic zonesT(Wallace, 1986) would help improve not only the

design of the monitoring GPS networks, but also

tectonic models (e.g., a block-and-fault model,

Hashimoto and Jackson, 1993) hence the under-

standing of crustal surface deformations associated

with both intra- and inter-plate tectonics.

The investigation of full-range tectonic processes is

very challenging, despite the recent realization of

nationwide continuous GPS monitoring for crustal

deformation in Japan. The behavior of the crustal

surface is influenced by various scale sources (in

space, time, and magnitude): intra- and inter-plate

interactions (e.g., Whittaker et al., 1992; Wang and

Suyehiro, 1999; Dragert et al., 2001), readjustments of

the crust near large seismic events (e.g., Heki et al.,

1997; Pollitz et al., 1998; Segall et al., 2000), tides

(e.g., Hatanaka et al., 2001; Kasahara, 2002), volcanic

and geothermal activity (e.g., Mogi, 1958), etc.

Arranging the monitoring GPS network in a hier-

archical manner preferentially along active tectonic

zones might be ideal, but it is impractical; most active

tectonic zones have yet to be fully characterized.

In addition, local or short-term details of crustal

surface deformations are often obscured by the

intricate physical makeup and local processes along

active tectonic zones, e.g., by transrotational shearing

(e.g., Kanaori et al., 1992; Dickinson, 1997) and by

various transient events that do not directly reflect

gradual and regional plate tectonics (Nur et al., 1989).

Measurement errors in our data are also troublesome

(e.g., Kato et al., 1998; Hatanaka et al., 2003).

A practical approach to analyzing complex crustal

deformation would be to focus on crustal deformation

on one particular scale range at a time, with the

premise that crustal deformation is a scale dependent

phenomenon that might be seen to be operating in a

more or less tangible unit of scale range. Such an

approach would allow a comparison of the dynamics

of a dlevel (scale range)T of our interest with that of theimmediate higher and lower levels in the presumable

nearly decomposable hierarchies of crustal structures

and processes (cf., Hierarchy Theory; e.g., Simon,

1962; Sollins et al. (1983) in O’Neill, 1988).

Here we are searching for inland tectonic zones in

Japan that can be seen to be active on the mesoscale in

the intermediate-term, and stretching the bounds of

possibility to observe them at the maximum attainable

resolution from the present nationwide GPS array.

dMesoscaleT in this study refers to a dimensionapproximately twice the local mean GPS station

separation distance and greater (approx. 70 to hundred

kilometers). Systematic shifts in the ITRF velocity

fields and two-dimensional instantaneous strain rate

anomalies are regarded as active tectonic zones

(ATZs) in this study. A set of robust and exploratory

analyses of the continuous GPS array enables us to

accommodate various irregularities in the data, to

identify the sharp geometry of ATZs on the mesoscale

nationwide, and to help decompose the multiscale

(b) Deceleration of upheaval(b) Deceleration of upheaval at Sakurajima V at Sakurajima Volcanoolcano

-202

W E

W E

W E

Station ID 960719Station ID 960719Station ID 960719

0

S N

S N

S N

0 200200200 400400400 600600600 800800800-2-2-202

D U

D U

D U

Time (days)ime (days)Time (days)

(cm)(cm)(cm)

-2-2-2

2

(Linear trend removed)(Linear trend removed)(Linear trend removed)w.r.r.t. WGS84.t. WGS84w.r.t. WGS84

Usu VUsu Volcanoolcano Mar Mar.2000 eruption.2000 eruption

Miyakejima VMiyakejima Volcanoolcano Jun.2000 eruption Jun.2000 eruption

(a) Ongoing T(a) Ongoing Tokai-Kanto okai-Kanto Slow Event Slow Event

PA

NANA/OH/OH

EU/AREU/AR

PHPH

Reference StationReference StationStations with MAD > MAD limitStations with MAD > MAD limit

3333oN

3030oN

128128oE 132132oE

3232oN

30'30'

3131oN

130130oE 131131oE

3232oN

131131oE

Fig. 1. Deformation velocity and acceleration fields (Example: 1998/7/18–2000/10/5). (a) Ongoing trend of Tokai-Kanto slow event. (b)

Deceleration of an upheaval at the Sakurajima Volcano. The upper-left insert shows major/micro tectonic plates: Eurasia (EU)/Amur (AR),

North American (NA)/Ohotsk (OH), Pacific (PA), and Philippine Sea (PH) plates.

Y. Toya, M. Kasahara / Tectonophysics 400 (2005) 27–53 29


intermediate-term processes, each of which may be

individually related to a governing tectonic process.

2. Method

Careful data quality analysis of GPS array (station

position data) in time and space makes possible the

refinement of deformation field data on the target

observational scale ranges: intermediate-term (~sev-

eral months to several years) and mesoscale, respec-

tively. Together it is important to realize that the

observable scale ranges of crustal deformation by the

existing GPS array are limited by the Nyquist

sampling criteria at the lower ends (twice a unit

sampling rate in time, provided that no higher

frequency periodic signals are present in the data,

and twice the local maximum station separation

distance, given no higher frequency undulation of

the deformation fields), and by the maximum ranges

of the data at the higher ends (the entire duration of

the case study period, and the whole length or width

of the Japan archipelago). In the same way, the

observation station arrangement plays a crucial role in

defining the local geometrical resolvability of ATZs

by the existing GPS array, given no high frequency

undulation of the deformation fields.

A temporal data quality analysis is performed at

first, to eliminate short-term noise, such as impulse

noise, additive seasonal variations and prominent

transient event noise, essentially to supply only

intermediate-term deformation rate signals to the

subsequent spatial data analysis. The deformation

fields as deduced from the intermediate-term signals

are then refined to reveal only mesoscale signals by

the application of robust smoothing and exploratory

spatial data analysis. The keys here are to recognize

the hidden structures and the exact type(s) of noise

present in the deformation field data and to apply a

suitable set of methods in handling them. As a

result of the temporal and spatial data quality

analyses, a reasonably uniform measure of deforma-

tion rates is achieved nationwide on the target scale

ranges. Using such a uniform measure of deforma-

tion rates nationwide, the continuous monitoring of

deformation rate changes, and the identification/

characterization of ATZs become feasible; they help

reveal where or which of the known tectonic (or

seismic) zones might be currently dactiveT on themesoscale.

2.1. Data

The nationwide permanent GPS network, the GPS

Earth Observation NETwork (GEONET), has been

operated by the Geographical Survey Institute of

Japan (GSI) since 1993 (Tada et al., 1997). Approx-

imately 6 years of continuous GPS station position

data on the ITRF97 (1997/6/25–2003/9/25 (UT)) were

obtained from the GSI web-site (http://www.gsi.

go.jp). The database was recently updated upon

significant reduction in systematic errors and

improvement in the database homogeneity as a whole

(Hatanaka, 2003; Hatanaka et al., 2003). Still, system-

atic errors (notably seasonal variations) exist in the

data, and their mechanisms are not entirely under-

stood. For example, regional-scale seasonal variations

in the data are known to be well correlated with the

seasonality of large subduction earthquakes near

Japan (Murakami and Miyazaki, 2001), the snow

loading cycle (Heki, 2001), etc., whereas the ampli-

tudes of such signals are commensurate with those of

baseline measurement errors in the array (Hatanaka,

2003). Sudden elastic strain signals are also trouble-

some in a study of interseismic deformation (e.g.,

Jackson et al., 1997). In view of the above concerns,

we attempted to eliminate prominent seasonal and

short-term noise from the data. The culled data sets

(presumably free of systematic errors and noise) are

then applied in the mapping of active tectonic zones.

2.2. Temporal data quality analyses

2.2.1. Removal of seasonal variations in temporal data

First, continuous daily recordings of horizontal

station positions are selected based on the criteria

listed in Table 1, and filtered with a five-point moving

median to reduce impulse noise in the time series. The

time series are then treated for removal of additive

seasonal variations. To do this, each time series is

carefully modeled with an equation consisting of three

terms: seasonality (annual and semiannual compo-

nents (e.g., Heki et al., 1997; Sagiya et al., 2000)),

drift (a second-order polynomial), a sudden disturb-

ance or an offset at time ts (a Heaviside function),

besides the residuals. The timing of offset ts is

http://www.gsi.go.jp

Table 1

Criteria for selecting continuous data

1. Data sets (stations) must belong to the permanent observation

network. No temporary campaign data are included.

2. Duration of data at a station must be longer than 2 years, in

order to estimate realistic or accurate seasonal patterns. For

this particular study, sampling time interval (dSWINT) is fixedfor 810 days (cf., Section 2.2.2).

3. The total number of observation days (dTNODT) in a dailystation position data set must be larger than 0.75 SWIN. If either

the data set for the East–West or North–South component of

horizontal deformation rates at a station does not meet this

criterion, the data for the station are not used for further

analyses.

4. There must be more than 2/9 TNOD for each successive SWIN/3

interval. Those unavoidable temporal gaps in the records are

linearly interpolated. This criterion together with the dMAD-limit(introduced in Section 2.2.2)T was effective in most cases to selectgenerally continuous data sets.


simultaneously determined while minimizing the

least-squares error to the model, by sliding ts along

the time-axis (with 1% increment of the whole

duration to reduce the computation time). When the

optimal fit is found, only the seasonal components are

subtracted from the filtered original time-series.

The second-order polynomial is considered for the

drift component of the aforementioned least squares

fitting (instead of a frequently used linear model). It is

employed to account for the effects from sizable

intermediate-term deformation rate changes, such as

ones observed near the Sakurajima Volcano and the

ongoing Tokai-Kanto slow event (e.g., ddeformationaccelerationsT, Fig. 1). At the same time, a Heavisidefunction is introduced in the model to help prevent the

creation of artificial sinusoids at a large sudden offset

in the data. However, the Heaviside function alone is

not sufficient to model various types of transient

events. Therefore, short-term irregularities, inclusive

of earthquake related displacements, are handled in a

different manner.

2.2.2. Systematic removal of short-term irregularities

Next, prominent short-term irregularities are sys-

tematically identified and removed. A dvelocityTestimate of crustal deformation is a practical expres-

sion for the mean deformation-rate for a given

observation period, or a linear fit to an observed time

series. Similarly, the second derivative of a second-

order polynomial fit to the time series can be regarded

as an daccelerationT of a possible nonlinear process fora well-modeled duration. Both approximations lack fit

when large noise or transient signals are present in the

data. Accordingly, the significance of irregularities is

evaluated based on the goodness of fit measures of

our approximations to the data.

The mean absolute deviation (MAD) is used to

measure the departure of observations from a poly-

nomial model, per component. MAD=(A|ri�r*|)/n,where ri is the residual displacement at time i (i=1, 2,

3, . . . , n), and r* is the sample median of the residualsafter the seasonality removal. The 96th percentile

(approximate upper limit of the bnormal rangeQ) of thegood-fit MAD population for the case study data was

selected as the MAD-limit: 0.25 cm for the velocities

(Fig. 2a) and 0.2 cm for the accelerations. A MAD

limit was defined so as to select only those data sets

(or stations) that fit well with our models. Those

stations with outlying MAD values above the limit

were found clustered around concurrent transient

events such as earthquakes and volcanic eruptions.

The rejected stations above the limit are marked with

square-and-cross symbols in the velocity field map,

e.g., Fig. 1. Also, the observational time-interval is

kept unchanged for the case studies to keep the

measure of irregularities unbiased (810 days each [cf.,

Table 1]). The longer the observation period, the less

significant a transient event appears.

The behavior of deformation-rate parameters:

velocity and acceleration, at a transient event was

evaluated using synthetic time series (e.g., Fig. 2b–e).

As the models demonstrated, the MAD limit, e.g., for

velocities (Fig. 2b, c, and e), worked effectively in

suppressing the maximum step height of elastic

signals (or its equivalent) in our data at ~1 cm per

component, inclusive of the residual error amplitudes

after the median filtering of the original time series.

The models also suggested that some slow events

could still be hidden in our data (Fig. 2e). A

comparison of the spatial distributions of MAD

between a linear model (a velocity field) and a

nonlinear model (e.g., an acceleration field) would

alternatively help locate such slow events, with

preferred nonlinear fits. Although it was almost

outside our case study period, the Bungo Channel

slow event (Hirose et al., 1999) could be identified in

this manner with a longer sampling time-window.

Nevertheless, we handle the effects from slow events

Synthetic ModelsCase Study Data

0 0.2 >0.4

MAD-limit for velocity = 0.25

Fre

q. (

NS

)

Fre

q. (

EW

)

MAD

poor fit

good fit

poor fit

good fit

App

aren

t v

eloc

ity

(

cm/y

r)

Ste

p h

eigh

t (

cm)

App

aren

t a

ccel

erat

ion

(cm

/yr

)2

Maximum

Duration of event (DE=various)

Sampling time-interval (SWIN=810days)

Time

(b)

(c)

(d)

Ste

p he

ight

(cm

)

Duration of event (days)200 400 600 800

1

2

3

4

5

Maximum apparent velocity (cm/yr) Corresponding maximum MAD (cm)

3

2

1

1

0.8

0.6

0.4

0.2

0.25

MAD limit

(e)

TP

(a)

Fig. 2. bLeftN (a) Histograms of MADs concerning the horizontal velocity estimates (East–West and North–South components) using the case

study data. Data with MADs greater than the MAD-limit (0.25 cm for velocities; cf., Section 2.2.2) are removed from the analysis. bRightN

Behavior of deformation rate parameters at transient events on synthetic time series. (b) Synthetic displacement records of hypothetical transient

events with a given offset-height and various durations (three time series, overlaid). (c) Corresponding apparent velocity responses around the

hypothetical transient events shown in (b). (d) Apparent acceleration responses around the hypothetical transient events shown in (b). A time

series record would be disturbed by a transient event for a duration dTPT=dSWINT+dDET, where dSWINT stands for the fixed sampling time-interval and dDET stands for the duration of a transient (slow) event. (e) A summary graph showing the maximum apparent velocities and thecorresponding maximum mean absolute deviations (MAD) (shown in contours) of synthetic time series as shown in (b). All models are

evaluated using a fixed size sampling time-interval, 810 days each.


and other subduction-related phenomena differently in

this study (discussed in Sections 2.3.3 and 2.3.4).

2.3. Spatial data analyses

Once the data become largely free of prominent

short-term noise, the focus is shifted to the inves-

Fig. 3. (a) Median, several EDA tools, and outliers. Outlier can be visu

histogram of absolute velocity vector lengths, for example (left figure). This

dextreme outlierT, which is greater than 3 IQR from the 75th percentileSchematic illustrations of the flow of robust smoothing process, using a de

the upper row of the illustrations, shown are the three steps of the smoothi

bStep IIN regularization of the observation grid and median filtering,

independent parameters, and post-filtering. Velocity fields are depicted in

dHNODCT indicates a nested imputation operation, described in the texoperation are: the minimum surface area, the maximum length of the si

sampling-window radius vs. nodal-point density after the imputation oper

point density is generally uniform when the sampling-window radius R is a

range of F1 sigma around an estimated point density for a given R. A mapplot the graph on the left. The reason for the preferred uniform point densit

separated by a distance of about 30 km and that they are anchored durin

robust smoothing scheme and a fixed-point smoothing operation (moving m

the true parameter distribution (a sine curve). Given specific ranges of (orig

the introduced scheme can provide a nearly even overall measure of

underestimate parameter values at local maxima and minima. (e) The ITR

Japan; cf., Fig. 4a) for 1998/7/18–2000/10/5. The original velocity field (bl

for comparison. Microscale irregularities of the original velocity field were

marked by a square symbol, and the areas labeled dAT (sketched in shade

tigation of spatial characteristics of the intermediate-

term deformation fields. The temporal data quality

analysis discussed in the previous section helped

identify and remove short-term noise, whereas some

spatial noise still remained in the data (e.g., Fig. 3a).

Through the application of robust smoothing and

exploratory data analysis (EDA), various properties of

ally identified in the ITRF velocity field (right figure), and in the

particular example of spatial impulse noise in the velocity field is an

line in the histogram. IQR stands for the interquartile range. (b)

formation field example with a narrow simple shear boundary. From

ng process: bStep IN imputation of the vector field for anti-aliasing,

and bStep IIIN representation of deformation rates in coordinate

map views and in profiles. The illustrations are not drawn to scale.

t (Section 2.3.2). Specific constraints applied during the HNODC

des and the proportion of the imputation triangles. (c) A graph of

ation (cf., Step I, b). The graph on the left illustrates that the nodal-

bout 35 km for the case study data. A vertical error bar indicates the

of Japan with circles on the right shows the sampling areas used to

y around R=35 km is likely that the original observation stations are

g the imputation operation. (d) Comparison between the introduced

edian) using simple one-dimensional models. The top graph shows

inal) observation station separation distances and signal wavelengths,

the target parameter distribution. However, our scheme tends to

F velocity fields from a small region in the case study area (central

ack arrows) and the smoothed velocity field (grey arrows) are shown

efficiently filtered out. (The location of the Matsushiro swarm area is

) indicate the general locations of tectonic boundaries.)

R

RAOutlierFreq.

25th percentile

Median

75th percentile

IQR*

>1.5 IQRaway fromthe 75th pct.

"Outliers"~ Upper hinge

~ Lower hinge

Histogram

Boxplot

Hinges

e.g.) Absolute vector length

R = Rigid blockA = Tectonic boundary

ED

A to

ols

(* IQR = Interquartile range)ITRF velocity field

Impulse noise

=

ATZ ATZHNODC

Step I: Imputation of the vector field for anti-aliasing

Step II: Regularization of the grid and 2-D median filtering

Step III: Representation of deformation rates in coordinate independent parameters, and post-filtering

Query point

Vel

ocity

fiel

dV

eloc

ity p

rofil

eV

eloc

ity fi

eld

Vel

ocity

pro

file

Vel

ocity

fiel

d

Hexagonal grid for pseudo strain rate calculation

Triangular grid from Step II, used for CMD and VLMD estimation

‘Impulse noise’

‘Edge’

y = MEDIAN ( x1...n

)A

Filter window, and CMD or VLMD estimation window

x1

x2 xn

x3

(The minimum grid spacing is reflected in thecoordinate independent parameter statistics.)

A

(a)

(b)


0100km

R = 35 kmR = 80 km

R = 35 km

20 40 60 800.02

0.03

0.04

0.05

0.06

Radius of sampling (km)

Den

sity

of p

oint

s (k

m-2

)

Map distance

Fixed-point operation

Introduced scheme

Par

am.

valu

eP

aram

. va

lue

Par

am.

valu

e True param. variation

Original GPS stations

Imputed station positions

Predicted trend

Velocities on original GPS stations

Smoothed velocity field on a triangular grid

Station 970816 w.r.t. WGS84Station 970816 w.r.t. WGS84(JUL18, 1998 ~ OCT5, 2000(JUL18, 1998 ~ OCT5, 2000

0 400400 800800Time (days)Time (days)

4

2

0

0

-5-5

-10-10

20

-2-2-4-4

5

3

MU

D (

cm)

UD

(cm

)N

S (

cm)

NS

(cm

)E

W (

cm)

EW

(cm

) Vel.= 2 cm/yrMAD = 0.1 cm

Vel.= -4 cm/yrMAD = 0.2 cm

Vel.= -1 cm/yrMAD = 0.4 cm

EQs within 50 km of the station

Spatial impulse noiseSpatial impulse noisewith clean temporal datawith clean temporal data

(c)

(d)

(e) A

Fig. 3 (continued).



the deformation fields become increasingly clear. Our

data generally appear to hold the following structures

within them: dDataT=dsmooth background (brigidQtectonic blocks)T+dmesoscale edges (active tectoniczones)T+dmicroscale or impulse noises (disturbedstations, isolated tectonic features and measurement

errors)T.EDA is an approach or philosophy of how to

examine the data rather than a set of analysis

techniques (NIST, 2002). The essence of EDA can

be perceived by contrasting it to classical data

analysis. In a classical (or confirmatory) data analysis,

a researcher would first select a deterministic or

probabilistic model, which consists of a set of

assumptions for a given data set. Some quantitative

expressions for the assumed model are then calcu-

lated, ultimately to develop a hypothesis about the

data (but strictly based on the model). Accordingly,

choosing a bgoodQ set of assumptions or a ’model’ isvital for an accurate interpretation of the data. EDA,

on the other hand, focuses on ddataT properties first,and looks for hidden data structures by utilizing

synoptical tools such as scatter plots, histograms, box-

plots, or any other graphical aid that might help

visualize important features in data that might other-

wise be missed out in a simplified deterministic model

of a classical data analysis. As a result of EDA, a

feasible model may be suggested by the data (NIST,

2002). The main aim of a data analysis is to

understand the given data, and the precision of an

analysis result only has true significance when it is

also accurate (Tukey, 1977).

2.3.1. Robust and exploratory spatial data analyses

Intermediate-term velocity fields in Japan are

generally homogeneous and highly directional, except

near active tectonic zones and scattered impulse noise.

At least this is a data structure that can be immediately

recognized in the ITRF velocity fields (e.g., Fig. 3a).

The velocity fields on a geocentric reference frame are

unique in the sense that they are free of the additional

and extraneous ambiguities of locally selected refer-

ence station(s). If there were no local crustal move-

ments, the mesoscale velocity fields would appear

dflatT (at least locally) and all vectors would have anearly equal length pointing in the same direction (or

all zero vectors). For example, a test for uniformity

(against a unimodal alternative of directional data;

Mardia and Jupp, 2000) could be applied to report the

highly concentrated nature of the velocity vector

azimuths. The more concentrated the vector azimuths

concerning a certain mean preferred orientation, the

more rigid a local tectonic block would be, provided

all vectors were non-zeros and had equal lengths. In

order to describe the detailed tectonic features at our

target scale of observation, however, it is not feasible

to use such classical statistical analyses. The data sets

were too sparse for the majority of our study area.

Here instead, robust smoothing and EDA are per-

formed to delineate mesoscale anomalies in the

velocity fields, with added assumptions about the

homogeneity, continuity, and the highly directional

nature of micro- to meso-scale velocity fields. Like-

wise, the mesoscale velocity fields are smoothed with

the median operative as described below.

2.3.2. Robust smoothing of the velocity fields

The median is the 50th percentile of ordered

sample statistics. It gives a more robust estimate of

central location (in statistics) than the sample mean,

and is resistant to extreme values or doutliersT(Barnett and Lewis, 1984) in data. A drobustTestimator would be insensitive to deviations from

assumptions about a given probabilistic model or

distribution (Huber, 1979). Meanwhile, our data (the

velocity fields) did occasionally contain outliers

(e.g., Fig. 3a). dAccommodationT but not manualremoval of such outliers is preferred (Barnett and

Lewis, 1984) where it is practicable. In order to

reduce (microscale) impulse noise but to preserve

(mesoscale) edges in an image (the deformation

fields), the use of a linear shift-varying filter (e.g.,

Kalman filter) or a nonlinear filter (e.g., median

filter) is a necessity (Huang, 1981). (This is because

signals in two-dimensional images are always

positive quantities and do not follow the dnormalstatisticsT (Frieden, 1979).) Therefore, taking fulladvantage of the median’s resistant attribute, the

velocity fields are smoothed in three steps: (I)

median imputation (filling in for missing values),

an anti-aliasing measure for the subsequent filtering

operations, (II) drobust smoothingT (Huber, 1979) bymedian filtering, and (III) visualization of the

deformation fields in several alternative and conven-

tional forms of coordinate independent parameters,

and post-filtering. Fig. 3b illustrates the overall flow


of the smoothing process. Most dmicroscale noisesTare polished away in steps (II) and (III), while

dmesoscale edgesT are embossed in the dsmoothbackgroundT.

In step (I), the velocity fields with microscale voids

are filled in by a nested median imputation scheme,

illustrated in the upper row of Fig. 3b. The scheme

may be described as a hierarchical neighborhood

operation with the median operative applied over

constrained Delaunay triangles where the centroid of

each triangle is the query point to be filled in

(HNODC). The goal of this operation is to completely

fill the case study area with nodal points as uniformly

as possible (Fig. 3c), as an anti-aliasing measure for

the subsequent smoothing operations. The triangles’

proportions and surface areas are constrained to

induce repulsion among the nodal points. Repulsion

of these points makes their distribution much more

regular than otherwise (Okabe et al., 1992). At the

same time, the sample median vector-components in

the dmarginal orderingT (Barnett, 1976) of thebivariate samples (generally independent x- and y-

vector components) from its vertices are assigned to

the query point at each triangle center. This median

vector calculation, provisionally selected for its

simplicity, gives reasonable median vector estimates,

when the circular mean deviation of the sample vector

azimuths is smaller than 458, i.e., when they aresamples from a highly directional velocity field. Some

of the locally disturbed stations are also separated out

in the process.

In step (II), two-dimensional median filtering,

robust smoothing is applied on the imputed velocity

fields from step (I). This operation is effective not

only to remove impulse noise (isolated microscale

irregularities) but also to preserve the sharp edges of

the robust signals in the velocity fields (active

mesoscale tectonic zones). Justusson (1981) issued a

detailed discussion on the statistical properties of a

median filter. The sampling grid is simultaneously

regularized in a triangular grid (dStep IIT in Fig. 3b).Each new grid node is assigned with a set of the

sample medians in the marginal ordering of x- and y-

velocity vector components: Vuv=MEDIAN [BuC],B={the nodal points in the study area from step (I)},

and C={N nodal points inside a circular sampling

window radius (SWR) of 35 km}. (The word

bsampleQ is used to mean ’batch’ hereafter, since the

observations of data after step (I) are no longer

statistically independent.) As a result, the isolated

noise with a surface area smaller than half of the

sampling window (pSWR2)/2 km2 is removed. (Theedge values within an SWR from the perimeter of the

study area are slightly extrapolated outward to abate

probable edge effects.) More precisely, a new value on

the regularized grid represents the majority (or NN/2)

of the member in set C (of N nodal point values).

However, the local nearest-neighbor distances

among the original GPS stations (LNND) enclosing

an imputation triangle varied regionally from 3.8 to 70

km in our data. The Hokkaido region was particularly

thin as for station coverage, so the LNND values were

generally large. The frequency distribution of the

LNND for the whole study area is unimodal,

positively skewed and has the median and the third

quartile of 25 km and 33 km, respectively. The

problem of irregular station coverage was tolerably

overcome by the anti-aliasing treatment of the velocity

fields performed in step (I). After the robust smooth-

ing in step (II), the nationwide distribution of

deformation rates was uniformly rendered at a

resolution close to the maximum attainable from the

existing GPS array (e.g., Fig. 3d). Visual inspections

of the actual velocity fields suggested that selecting

the SWR of 35 km was reasonable for signals in our

study area, as would be reevaluated later in a

confirmatory study (Section 2.3.4). The results, e.g.,

Fig. 3e, suffice for our exploratory objective.

The median operations would leave a plateau

where spatial parameter distributions were nearly

constant. Such a plateau defines the extent of a drigidTtectonic block, and its sharp edges portray active

tectonic zones. Along a wide active tectonic zone

(N2SWR), the terracing of parameter variations,

byproducts of the median operations, is anticipated.

Still, the byproducts would have dimensions inher-

ently smaller than 1 SWR and larger than the

minimum size of the sampling grid-distance defined

in step (II). So, now the idea is to filter out those

artefacts in that range.

In step (III), the smoothed velocity fields from step

(II) are first transformed into several coordinate

independent parameters. Then, additional median

filtering with the same-size smoothing window as in

step (II) is applied on each spatial parameter

distribution to remove the artefacts from the previous


step. Changing the shape of a filtering window (e.g.,

circular or rectangular) or of the sampling grid (e.g.,

triangular or square) did not substantially change the

final case study results. The robust signals were

coherent regardless.

2.3.3. Systematic identification of active tectonic

zones

Anomalies in the spatial distribution of deforma-

tion rates were expected in two general conditions: (i)

proximity to disturbed stations and isolated micro-

scale irregularities, and (ii) proximity to active

tectonic zones. The condition (i) was easily noticed

as impulses or scattered noises in the fields, when it

did not coincide with the condition (ii). The noise (or

outliers) in condition (i) was efficiently removed (or

daccommodatedT; Barnett and Lewis, 1984) by therobust smoothing. Conversely, the condition (ii) was

made prominent partly by mapping the spatial

distribution of circular median deviation (CMD) for

the smoothed ITRF velocity fields. CMD=MEDIAN

(|p�|p�|hj�h*|||), where hj is the jth vector azimuth( j=1, 2, 3, . . . , n) in a sample from the smoothingwindow of step (III), h* is the sample median, and theoperands (inside the parenthesis) are the ordered

statistics of the minimum angular distances between

the median and sampled vector azimuths (p. 19,

Mardia and Jupp, 2000). Also, another useful param-

eter was the vector-length median absolute deviation

(VLMD) for the same velocity fields. VLMD=ME-

DIAN (|Lk�L*|), where Lk is the kth vector length(k=1, 2, 3, . . . , n) in a sample from the smoothingwindow of step (III) and L* is the sample median.

CMD and VLMD are median deviations of the

principal velocity vector components: azimuths and

lengths. Both CMD and VLMD discussed here are

specific to the ITRF velocity fields and are independ-

ent of the orientation of the geographical coordinates.

A comparison between CMD or VLMD distributions

with the original velocity fields help us realize that the

apparent bdeviationsQ do in fact represent dsystematicshiftsT in the velocity fields, or mesoscale structuralboundaries. Fig. 4 shows their spatial distributions.

The histograms on the color-scale bars in Figs. 4a

and b represent the frequency distributions of CMD

and VLMD for the whole case study area. The

overall shape of the frequency distributions is

apparently dabsolutely outlier-proneT (Green, 1976).

We realize, however, that despite the continuous

appearance of the overall frequency distribution,

there must be a nonrandom data structure within it;

the geographical regions corresponding to the pop-

ulations near the lower end of the overall frequency

distribution should represent originally claimed

drigidT tectonic blocks (R), and the other geograph-ical regions corresponding to the populations with

longer tails under the overall frequency distribution

should portray active tectonic zones (A). A perfectly

drigidT tectonic block (R) and an active tectonic zone(A) are theoretically ddisjoint.T Accordingly, theoverall frequency distribution might be interpreted

as a dcontaminated distributionT (Barnett and Lewis,1984): cja(1�k) R+kA that observations cj ofdeformation rate in a sample ( j=1,2, . . . ,n) wouldarise from a mixture of R and A , where

0bkb1(k=contamination fraction), dRT=the popula-tion for all drigidT tectonic blocks, dAT=the contam-inants or the populations of active mesoscale tectonic

zones.

Nonetheless, the active tectonic zone signals (A) in

the actual field data might include both signals: ones

that originate from inland tectonic processes and ones

that are directly from contiguous subduction zone

processes with some overlaps in between. They are

practically inseparable; they have very similar wave-

lengths, except that the latter would be noticeable

along the Pacific coast in Japan. Particularly, the

geometry of mapped active tectonic zones with

parameter values above the 75th percentile of their

frequency distribution or the dupper hingeT (Tukey,1977) coincides well with some known tectonic

features in the study area (Fig. 4). Accordingly,

deformation rate anomalies with parameter values

above the upper hinge are specifically referred as

dATZsT thereafter. The background map in Fig. 4cillustrates a percentile summary of CMD and VLMD

distributions, named dMD2T, highlighting the geo-graphical areas with CMD or VLMD parameter

values greater than their 75th percentiles. In that the

mesoscale anomalies were very powerful and con-

centrated in confined areas, slightly shifting the center

of the color-scale (either hue or value of the color) in

Fig. 4 did not significantly change the overall

appearance of the resolved ATZ distribution.

CMD and VLMD distributions (or MD2) hint at

the locations of ATZs. Now, two-dimensional instan-

Fig. 4. Maps of (a) circular median deviation (CMD) and (b) vector-length median deviation (VLMD) of the ITRF velocity fields in Japan.

Parameter values depicted in the maps are the means of the two 810-day periods before and after the 2000 W. Tottori earthquake. The histogram

and box-plot for each parameter are shown on the corresponding color-scale bar. The base of an arrow pointing to the right on the color scale

indicates the upper-hinge value for the given parameter. A diamond-shaped box over the CMD map indicates the region of the velocity field

shown in Fig. 3e. (c) Tectonic map of Japan, over a map of MD2 or a percentile summary of the CMD and VLMD distributions (cf., Section

2.3.3). Symbols denote active volcanoes (in red triangles), Setouchi Inland Sea (in black cross stripes), and the major tectonic zones (in solid and

dashed lines), which include: the Kuril Trench (KT), the Japan Trench (JT), the Sagami Trough (SaT), the Suruga Trench (SuT), the Nankai

Trough (NT), the Median Tectonic Line (MTL), the Tsuruga Bay–Ise Bay Tectonic Line (TITL), the Itoigawa–Shizuoka Tectonic Line (ISTL),

the Honjo–Matsushima Tectonic Line (HMTL) (Tada, 1986), the Niigata–Kobe Tectonic Line (NKTL) (Sagiya et al., 2000) in grey shade, and

the Oga–Ojika Seismic Zone (OSZ) (Mogi, 1985).



taneous strain rates are mapped to resolve the

characteristics of intermediate-term deformations

along individual ATZs. The smoothed velocity fields

from step (II) are spatially differentiated to give

coordinate independent strain rates: dilatation, max-

imum-shear, and rotation (Terada and Miyabe, 1929;

Tsuboi, 1930). All of these strain and rotation rate

distributions together describe the trend of small

strains associated with an individual ATZ. Their

absolute quantities, however, are inexact (often under-

estimated, cf., Fig. 3d) along ATZs and thus they are

named dpseudo strain ratesT.

2.3.4. Evaluation of the geometrical resolution of

ATZs

Before applying the introduced ATZ-mapping tool

to the actual field data, its geometrical resolvability is

confirmed by calibrating it against synthetic tectonic

boundary models: (a) simple-shear and (b) pure-shear

(or a pair of irrotational zones) models, e.g., Fig. 5.

No dilatational strain is expected along a simple-shear

boundary, and no rotation is expected along an

irrotational zone. The color-scales of pseudo strain

Fig. 5. Calibration of the introduced ATZ-mapping tool against synthetic tec

pure-shear (a pair of irrotational boundaries) model. Dilatation (D)=(Bu(R)=[(Bu/Bx�Bv/By)2+(Bu/By+Bv/Bx)2)]0.5. No dilatational strain is expecan irrotational boundary. Three types of errors are shown as examples: a de

On the right, two calibration test results for our study area are shown usin

rate maps are set so as to satisfy the above require-

ments in several synthetic models, and to highlight the

mapped areas with absolute parameter values above

the upper hinge of their frequency distributions using

the case study data (cf., Fig. 4). Long-wavelength

deformation signals and some small measurement

errors (after step (II)) are suppressed below the upper

hinge limit. In that most ATZ anomalies were power-

ful on the mesoscale, the general appearance of the

resultant maps was not substantially changed by the

slight tuning of the color scale around the upper hinge

in the case study data.

It is possible to tune the overall intensity of the

ATZ signals. For instance, a large proportion of the

gap error, dGT in Fig. 5b, is avoided by adjusting themean nodal point density in step (I) (cf., Figs. 3b and

c), and the sampling grid spacing in step (II). In any

case, deflection errors, dLT in Fig. 5b, however, areinevitable within F1 SWR. Also, the widths of theATZs are adequately resolved when they are greater

than 2 SWR, and evenly recovered when they are

greater than twice the maximum LNND in our study

area. Testing the mapping tool against multiple

tonic boundary models: (a) wide simple-shear model and (b) narrow

/Bx+Bv/By). Rotation (x)=0.5*(Bu/By�Bv/Bx). Maximum shearted along a simple-shear boundary, and no rotation is expected along

flection error (L), a gap error or a loss of detail (G), and noises (NO).

g the models of types (a) and (b).


synthetic models such as those shown in Fig. 5 helps

confirm that any powerful wide ATZs (N2 SWR) and

non-clustered and non-oscillating narrow ATZs (b2

SWR) are tolerably recovered by the introduced

scheme from the present GPS array. Visual inspec-

tions of the actual velocity fields in our study area

suggested that the deformation rate anomalies were

neither critically clustered nor oscillating at scales

immediately below the mesoscale.

The introduced scheme has an advantage over

other fixed-point smoothing operations, e.g., a mov-

ing median without anti-aliasing treatment on the data.

Our method is more efficient than the others

mentioned in illustrating the spatial parameter varia-

tions evenly over the irregularly distributed observa-

tion stations in our study area. This property is

Fig. 6. Comparison between the dilatational strain rate distribution maps o

method employed in Sagiya et al. (2000) (c, d, and e). (a) Dilatational p

geometrical resolvability test on irrotational boundaries (cf., Section 2.3.4)

rate map of Japan, from Sagiya et al., 2000 (reproduced, with permission, f

(c) using the least-squares inversion method on the data for 1997/1/1–1999

data quality analysis (cf., Section 2.2). dST-limitT or standard deviation limirregularities. The ST-limit is set to 0.33 cm (=1.3�0.25 cm) considering2003) and that the MAD-limit for velocities is set to 0.25 cm for the case st

test on irrotational boundaries (Section 2.3.4) using the least-squares invers

observational errors (Eq. (3), p. 2309, Sagiya et al., 2000) in the synthetic

on the actual field data property. Dots on the maps denote GEONET stati

demonstrated in a set of simplified one-dimensional

models, shown in Fig. 3d. Let us suppose that the

upper graph in Fig. 3d shows the true parameter

distribution (a sine curve). Although the introduced

scheme tends to underestimate parameter values at

local maxima and minima, it can provide a nearly

even measure of target parameter distribution, given

specific ranges of signal wavelengths and the original

observation station density.

Also, our method does not employ the variance–

covariance information of the GPS data at the

moment; therefore, the results are not directly affected

by the small but inevitable systematic errors in the

variances, which can exist as error propagates in a

large-scale network (Vanicek and Krakiwsky, 1982).

Our results are predominantly affected by the true

f Japan generated by the introduced method (a, b) and ones by the

seudo strain rate map for 1997/1/1–1999/6/30. (b) The result of a

using the same observation stations as in (a). (c) Dilatational strain

rom n Birkhauser Verlag, Basel). (d) A reconstruction of the map in/6/30, as in Sagiya et al. (2000), after the application of the temporal

it is applied in place of the MAD-limit to eliminate the temporal data

that STc1.3 MAD when the distribution is bnormalQ (MathWorks,udy data (Section 2.2.2). (e) The result of a geometrical resolvability

ion scheme, applied over the same observation stations as in (d). The

data are assumed to be 0.13 cm for both x- and y-components, based

ons used in the strain rate calculations.


(immeasurable) accuracy of the available station

position data, besides the measurement errors men-

tioned earlier in this section.

The improvement of the geometrical resolution of

ATZs using the new scheme is clear, compared with

the results by other methods, for example, ones by

Sagiya et al. (2000). Their dilatational strain rate map

of Japan is reproduced in Fig. 6 and compared with

our results. They used a least-squares inversion

scheme, a slightly modified version of the method

introduced in Shen et al. (1996), on the GEONET data

for January 1997–June 1999. The results by their

method appear slightly blurred. That is likely due to

the Gaussian spatial noise assumption in the least

squares method and due to their disregard of the

highly irregular observation station arrangement in the

study area. In addition, the prominent spatial noise,

impulse noise, does not have a clear relationship with

the geographical distribution of temporal white noise

amplitudes in the data. Hokkaido region in Fig. 6 was

left blank after the temporal data quality analysis

(Section 2.2); there would have been a risk of spatial

aliasing affecting our results due to thin coverage of

usable stations in the area for the specific study

period.

2.4. Analysis plans for spatio-temporal variations of

deformation rates on ATZs

The regional and temporal variations of the

deformation fields are monitored with pseudo strain

rates. Two types of analyses are considered: (1)

comparisons of the spatial parameter distributions

before and after a reference time, e.g., the time of a

large earthquake, and (2) continuous (retrospective)

monitoring of spatial parameter distributions. The

observational time window was kept unchanged for

the case study to keep the measure of deformation

rates unbiased (cf., Section 2.2.2). For a type (1)

analysis, the identical set of observation stations is

used to compare the strain rate distributions for the

two successive non-overlapping time periods (810-

day each) before and after the 2000 Western Tottori

earthquake. In case of a type (2) analysis, the

observational time-window (810-day long) is moved

along the time-axis in increments of about a month

(30 days), and the changes in parameter strengths are

systematically recorded at the end of the time-

window. All available observation stations were used

for type (2) analyses, except for data with large

irregularities that were automatically removed from

the analysis by the application of the MAD-limit (cf.,

Section 2.2.2). A series of geometrical resolvability

tests with synthetic velocity fields (cf., Section 2.3.4;

Supplementary materials) demonstrated that not using

the complete set of observation stations for different

time steps did not severely affect the analysis results.

The mean of the upper hinge values of a given

parameter distribution for 810-day observation peri-

ods before and after the 2000 W. Tottori earthquake

was selected as the reference of the parameter

strengths.

3. Style of deformation along active tectonic zones

Mesoscale tectonic zones on the four main islands

of Japan were outlined in the maps of CMD, VLMD,

and MD2 (Fig. 4), and the characteristics of current

concentrated deformation were illustrated in the

pseudo strain rate maps (Fig. 7). Both types of

anomalies appeared to overlap geographically.

Although the definition of ATZs was rather qualita-

tive, the signals were as powerful as can be visualized

as the systematic shifts in the ITRF velocity fields and

as coherent strain rate anomalies. The ATZs were

preferentially located along some known tectonic

zones, chains of active volcanoes and low seismic

velocity anomalies in the crust and upper mantle. The

majority (60–70%) of the mapped ATZs was con-

tinuously active for the whole 6-year case study

period, while the remainder continued to operate

sporadically.

3.1. Dilatation

The Japanese islands are under compression from

the subduction of the Pacific and Philippine Sea plates

(e.g., Kato et al., 1998). Near trench-parallel belts of

areal contractional (negative dilatational) strain rate

anomalies were noticed for almost the entire length of

the island arc (Fig. 7a). The strain rate anomalies were

persistent for the whole case study period in the

Shikoku Island, along a belt from near Matsushiro to

Niigata, and along the volcanic front in Tohoku and

eastern Hokkaido.


Contractional strain rates were exceptionally

prevailing on the ATZs in much of Shikoku, Kinki,

and southwestern Chubu regions before the 2000 W.

Tottori earthquake (MJMA 7.3). In the following year,

the Geiyo Earthquake (MJMA 6.7) also occurred 140

km southwest of the W. Tottori event (Fig. 4a). The

contractional strain rates at the crustal surface

relaxed about 20% after the sequence of the earth-

quakes (Fig. 7a). Meanwhile, a broad area from

Kinki to Kanto appeared to be influenced by the

accelerating Tokai-Kanto slow events (Fig. 1a) in the

sense that it would encourage relaxation of the

contraction in the affected upper plate areas. Sim-

ilarly, there was an episode of intensifying areal

contractional strain rates near the Sendai plains, a

20% increase (Fig. 7a), before the recent sequence of

large earthquakes in the vicinity: 2002/11/3 Miyagi-

Oki earthquake (M6.3), 2003/5/26 Miyagi-Oki earth-

quake (MJMA 7.1) and 2003/7/26 Northern Miyagi

earthquake (MJMA 6.4).

Positive dilatation was remarkable near the Sakura-

jima Volcano, e.g., for 1998/7/18–2000/10/5 (Fig. 7a),

and the deceleration of an upheaval was evident in the

acceleration field (Fig. 1b). An acceleration field

associated with a permanent deformation, which

would be proportional to a set of driving forces in a

nearly uniform medium, is an interesting subject to

study in detail. However, it is beyond the scope of this

paper, and will be explored elsewhere.

3.2. Shear

Fig. 7b shows the distributions of maximum shear

strain rates. Large shear strain rates were detected in

several areas: over much of Shikoku and the

southeastern Kyushu islands, near the Atotsugawa

fault, in the Matsushiro–Niigata area or the northern

Fig. 7. Pseudo strain rate maps: (a) dilatation, (b) maximum shear, and (c

(Period 1), and the bottom one is for 2000/10/6–2002/12/25 (Period 2). Th

value of a given absolute parameter frequency distribution. Temporal variat

in two selected areas: Zone 1 and Zone 2, are graphed in the inserts for (a)

illustrate the fluctuations of the sample medians of maximum shear pseudo

line illustrate the fluctuations of the corresponding IQRs. IQR stands for t

records (cf., strain rate calculation points, Fig. 3b), and the time series o

Section 2.2.2) is changing with time. Labels in the inserts for (b) denote: 20

earthquake (M1), 2003/5/26 Miyagi–Oki M7.1 earthquake (M2), and 200

denote: Shimanto metamorphic belt (Shimanto), Abukuma metamorphic t

(data sources: Japan Meteorological Agency and their affiliates (2003), an

NKTL, near the Sagami Trough, along the volcanic

front in Tohoku (Nakajima et al., 2001) and eastern

Hokkaido, and above a low seismic velocity

anomaly in the Hidaka range (Takanami, 1982;

Murai et al., 2003).

Shikoku and southern Kyushu are extensively

strained in the intermediate-term, but with very little

MN3 seismicity. Particularly, the Nankai forearc sliver

to the south of Setouchi or the Median Tectonic Line

(MTL) is in a fast right-lateral shear with respect to

the dRigidT Chugoku block (Fig. 8) and internallybrotatingQ (Fig. 7c; cf., Section 4.3). Fig. 8 showsMTL-parallel and -normal components of deformation

rates in the Shikoku Island with respect to the

Chugoku block. The apparent aseismic movement

on MTL is roughly 5 mm/year right-lateral, which

agreed with the rate estimated by others (Miyazaki

and Heki, 2001; Tabei et al., 2003). What is striking is

that both MTL-parallel and -normal deformation-rates

on the Shikoku Island decreased several millimeters

per year after the 2000 W. Tottori earthquake (upper-

right graphs in Fig. 8). This observation can be

compared to the aforementioned decrease of areal

contractional strain rates around the turn of the

century (Fig. 7a). Both components of the deforma-

tion rates along the MTL contained parts of the

trench-normal strain rate changes, because of the

obliquity of the MTL with respect to the Nankai

Trough (lower-left map in Fig. 8).

Southwestern and northeastern Japan are in colli-

sion at central Japan on a plate boundary between the

Amurian and North American plates (Miyazaki and

Heki, 2001). The rate of convergence is approxi-

mately 2 cm/year in the EW direction, derived by

estimating the relative drigidT block movements acrossan ATZ near the junction of the Itoigawa–Shizuoka

Tectonic Line (ISTL) and the NKTL (Fig. 9). This

) rotation. The upper map of each pair is for 1998/7/18–2000/10/05

e base of an arrow drawn on a color-scale indicates the upper-hinge

ions of dilatational and maximum shear pseudo strain rate parameters

and (b) on the right. Thick lines in the time series (the insert for (b))

strain rates in Zones 1 and 2, and two thin lines paralleling a thick

he interquartile range. dNT stands for the number of grid nodes withf dNT illustrate how the density of usable observation stations (cf.,00/10/06 W. Tottori earthquake (WT), 2002/11/03 Miyagi–Oki M6.3

3/7/26 Northern Miyagi M6.4 earthquake (M3). Labels on map (c)

errane (Abukuma), and Hidaka range (Hidaka). (d) Seismicity map

d Utsu (1982)).

Maximum Shear Pseudo Strain Rate

0.5

1.5

1

2x 10

-7

0

(Average of Period 1 and 2)MTL normal

MTL parallel

0 M

TL

0 M

TL

AA

NTNT

3

2

1

0

MTL normalMTL normal

Con

trac

tiona

l v

eloc

ity w

.r.t.

'A'

(

cm/y

r)

50 100 150 200 3

2

1

0

MTL parallelMTL parallel

Distance from 'A' kmW

este

rly

vel

ocity

w.r.

t. 'A

'

(cm

/yr)

decrease { Vel.(Period2) - Vel.(Period1) > 0 }increase { Vel.(Period2) - Vel.(Period1) < 0 }

MTL MTL A A

0

Deformation Rate:

a few mm/yr

MTLMTLForearcForearc SliverSliver

r

MTL

6.56.5 cm/m/y

NT

Cont. 3x10Ext.

-7Principal Strain Axes

Shikoku

(Convergence rate, Miyazaki and Heki, 2001)

/yr

/yr

Fig. 8. Crustal deformation in Shikoku region. Shown are Median Tectonic Line (MTL) parallel and normal components of the velocity fields

with respect to the drigidT Chugoku block. The group of stations in the box with cross-stripes along A–A line was considered as the fixedreference. On the right, two sets of velocity field profiles are shown. Period 1=1998/7/18–2000/10/05. Period 2=2000/10/06–2002/12/25. Two

things can be noted. (1) Small right-lateral slip along the MTL was apparent, 5 mm/year at the most. (2) There was an orderly decrease in the

deformation-rates (both MTL parallel and normal components) on the forearc in Shikoku around the turn of the century.


result agrees with the estimate by others (Miyazaki

and Heki, 2001; Hirahara et al., 2003), determined by

other means. Fast creep movements along the

Atotsugawa fault on the NKTL appeared to be driven

by such a fast convergence in the area. When the

relative velocity vector was projected onto an NKTL

segment near the Atotsugawa fault with a strike of

N60E, a rapid right-lateral shear (1.6 cm/year) and a

fault-normal contraction (1.3 cm/year) were detected

for 1998/7/18–2000/10/5, for example. The median

absolute deviation for both components was ~0.35

cm/year. GSI (1997), otherwise, reported local varia-

tions of creep rates along the central portion of the

Atotsugawa fault: 1.5 cm/year for a fast moving

segment and non-creeping at a position 15 km west of

it. These estimates were based on multiple precise

distance measurements with several 1–2 km baselines

across the fault. The last large earthquake to occur in

the area was the 1858 Hietsu earthquake (M7)

(Usami, 1996).

3.3. Rotation

Rotational ATZs were noticeable along the NKTL

(clockwise) and along the Pacific. Several clockwise

and counterclockwise pairs of rotational ATZs were

perceived in areas along the Pacific: the Shimanto

metamorphic belt (southern Kyushu to Shikoku-Kii),

Tokai, Sagami, the Abukuma metamorphic terrane to

the Kitakami mountains, and the Hidaka range to the

volcanic front in eastern Hokkaido (Fig. 7c). The

direction of maximum compressive stress, as deduced

from the focal mechanisms of shallow inland earth-

quakes, is known to be the same as that of the plate

convergence (E–W) in northeastern Japan, while it is

near trench-parallel (SW–NE) (Wang and Suyehiro,

1999) and occurs at an angle of about 458 to the plateconvergence direction in southwestern Japan (McCaf-

frey, 1993). Supposing that an in-between block of a

rotational ATZ pair was compressed faster than the

surrounding areas in the fashion depicted in the insert

Fig. 9. Pseudo strain rate maps of central Japan, for 1998/7/18–2000/10/05. Shown are, from the left, dilatational (D), rotational (x), andmaximum-shear (R) components. The base of an arrow drawn on a color-scale indicates the upper-hinge value of a given absolute parameterdistribution. The spatial distributions of the dilatational and maximum shear strain rates across two anomalies are also shown in profiles. A red

line on the profiles indicates the upper hinge value for the corresponding parameter. The active faults are shown in grey lines on the maps (active

fault data source: Research Group for Active Faults of Japan, 1991).


of Fig. 7c, then, the sense of rotation on the ATZ to

the right of the in-between block facing the compres-

sion direction would rotate clockwise and that of the

left would rotate in a counterclockwise direction.

Given such a configuration, it is possible to recognize

that landward crustal movements of the in-between

blocks were prevailing during the whole 6-year

observation period, except for a pair in Tokai that

indicated a seaward transient crustal movement. The

trend and timing of the crustal surface movement in

Tokai (Fig. 1a) matched that of the ongoing Tokai

slow earthquake (Ozawa et al., 2002).

4. Discussion

Our empirical observations, refined by the appli-

cations of robust smoothing and exploratory–confir-

matory analyses on the irregular data sets,

demonstrated that the primary features of the inter-

seismic crustal deformation in Japan can be described

in terms of two overlapping operative processes: (1)

the regional-and-steady mode of strain accumulation

(cumulative effect of distant tectonic forces) and (2)

the local-and-transient mode of strain accumulation

(individually linked to an imminent or concurrent

sequence of large tectonic events, both inland and

offshore).

Mesoscale intermediate-term deformation signals

(here altogether recognized as of ATZs) often

account for slow earthquakes (e.g., Hirose et al.,

1999), post-seismic deformations (e.g., Heki et al.,

1997), elastic strain accumulations and permanent

internal deformations in the upperplate areas. ATZs

accommodate interseismic deformation of various

forms: elastic strain accumulation (Jackson et al.,

1997), creep along a confined zone of crustal

weakness (e.g., GSI, 1997), and wall-block perma-

nent deformation (Sibson, 2002). Superposed upon

these localized inland crustal movements, there are

broader tectonic loading signals of various scales

from the contiguous major plate boundaries in

Japan. Widespread disagreements between regional

instantaneous geodetic strain rates (�10�7/year)

In space: MESOSCALE (70~several hundred kilometers)In time: INTERMEDIATE TERM (several months to years)

Our field of view / Observational scale range

Operational scales of interseismic crustal deformation

SPACE

long(several-100s years)

intermediate (months-several years)

short(seconds-months)

large(100s-1000s km)

medium(10s-100s km)

small(0-10s km)

Our field of view

Static stress-change

effect dominant

TIME

Regional-and-steady processLocal-and-transient process

Operative / characteristic scales of crustal deformation in our field of view:

Highly heterogeneous

mixture of effects + noise

Dynamic stress-change

effect dominant

Fig. 10. Summary diagram of the operational scales of interseismic

crustal deformation with respect to the observable range by the

existing GPS array. Our observable scale-range is limited within the

rectangular box in the center, labeled dOur Field of ViewT. Thediagram would help distinguish the regional-and-steady deforma-

tion signals (of scales around the solid circle) from local-and-

transient deformation signals (of scales around the open circle).

Local-and-transient strain rate changes are presumably caused by

stress-changes accompanying the bco-seismicQ phenomena prevail-ing on certain scale-ranges, labeled in the background. bCo-seismicQin this context might include immediate precursory deformation and

immediate post-seismic deformation (both fast and slow).


(Kato et al., 1998; Sagiya et al., 2000) and local

geologic strain rate estimates along active fault

traces (�10�8/year) (Nohara et al., 2000) are oftenattributed to such interseismic elastic strain accumu-

lation due to broad tectonic loading from the

contiguous subduction zones, where only small

portions of the differences actually contribute to

the permanent strains on many individual faults.

(Additionally, the fact that not all active microscale

or blind faults are identified in the crust might

explain a part of the large disagreements.)

Subduction effects (on both meso- and macro-

scales) should be removed from our data to correctly

assess the upperplate and intraplate deformations

(personal communication with several at IUGG,

2003). However, separating these effects presents

quite a challenge, as Japan is situated at the

confluence of several major tectonic plates. If one

were to identify and remove various subduction

effects, it would be necessary to perform the tasks

comprehensively; otherwise, it could merely create

biases in one’s interpretation of inland tectonics. The

maps of coordinate independent deformation-rate

parameters (Figs. 4 and 7) alternatively helped

identify mesoscale areas of disturbances or ATZs in

the upperplate that likely resulted from both intra- and

inter-plate tectonics. The resolved geometry and

characteristics of the ATZs might be utilized in a

tectonic model (e.g., Hashimoto and Jackson, 1993)

and could provide an improved understanding of

heterogeneous and non-isotropic mesoscale tectonic

processes in the near future.

4.1. Geometry and origin of inland ATZs

The geometrical agreements among the mapped

ATZs, chains of active volcanoes, and low seismic

velocity anomalies in the lithosphere are apparently

due to their common weakness on the mesoscale.

Moderate to large inland earthquakes (M5.7–8.0,

Db=20 km, in Japan (Zhao et al., 2000)) also tend

to occur near such preexisting weaknesses in the

crust (Zhao et al., 2000; Sagiya et al., 2000). The

weakness is believed to come from a high water

content in the shallow crust originating from the

dehydration of the subducted slabs (Nakajima et al.,

2001; Iio et al., 2002; Hyodo and Hirahara, 2003).

The presence of partial melt materials in the upper-

most mantle, e.g., beneath the volcanic front in

Tohoku (Nakajima et al., 2001), might be another

contributing factor for the relative structural weak-

ness on the mesoscale. Leaving aside the issue of

whether these weak zones constitute micro-plate

boundaries, they were apparently more sensitive to

ambient stress changes than the neighboring drigidTblocks. The apparent weakness on the mesoscale,

however, does not necessarily imply the same

quality for dmicroscaleT ATZs. Our observations arelimited to the scale-range in our field of view (Fig.

10). Similarly, the apparent behavior of crustal

surface materials whether it is ductile or brittle

critically depends on the observational scale (e.g.,

King, 1983).

A focused strain rate anomaly with its instability

apparent in a certain geometric condition of tectonic

boundaries, e.g., a triple junction on land (King,

1983; Gabrielov et al., 1996), might imply a stress


concentration. For example, the 1965–1967 Mat-

sushiro earthquake swarm area appeared to be

located near a junction of three mesoscale ATZs

(Figs. 3e and 4a). With southwestern Japan in

collision against the northeastern half (Fig. 9), the

localized stress near Matsushiro was possibly close

to its critical state in 1965 and eventually developed

into an energetic ductile deformation. The source of

locally dexcess (continuously been replenished)Tseismic energy-inputs during the swarm (Kisslinger,

1968) might have been the momentum in such a

ductile deformation. Expansive strains in the NS

direction were distinctive of the swarm episode,

which also matched well with the concurrent

moderate seismic events’ mechanisms (Kasahara

and Okada, 1966). It is likely that water eruptions

and other unusual phenomena were secondary to

such a diffuse process. In addition, the 1964 Niigata

earthquake (224 km north–north–west of Matsush-

iro) appeared to trigger the Matsushiro swarms, as

witnessed in the migrating pattern of diffused

seismicity from Niigata to Matsushiro (Mogi,

1988). In general, prominent ATZs, such as those

near Matsushiro and Akan in Fig. 4a, are suggestive

of well-developed tectonic zones, highly strained

and heterogeneous areas, where continued readjust-

ments and ductile deformation might possibly be

taking place on the mesoscale. Further investigations

of the swarm areas might be necessary to confirm

the above conjecture.

4.2. Subduction-induced strains on ATZs

Tectonic stresses in the overriding plate of a

subduction zone in the absence of back-arc spreading

are critically influenced by the locking and unlocking

of the adjacent subduction fault (Whittaker et al.,

1992), and the stresses fluctuate with time over many

earthquake cycles because of such a locking-and-

unlocking mechanism (e.g., Wang and He, 1999).

Temporal fluctuations of the stresses in turn induce

strain rate changes in the overriding plate that may be

observed by geodetic means. In our 6-year GPS

observation period, which was much shorter than the

interseismic period of a large characteristic earthquake

such as the Nankai earthquake, we still perceived at

least two apparent modes of strain accumulation along

the island arc. This is illustrated in the summary

diagram of operational scales of interseismic crustal

deformation, Fig. 10.

(1) Regional-and-steady mode (scales around a

solid circle in Fig. 10). About 60–70% of the

mapped inland ATZs or strain rate anomalies

were perceptible for the whole 6-year observa-

tion period; the overall pattern (the distribution

and the trend) of the anomalies did not

significantly change over time nationwide.

These steady strain rates presumably reflect

the gradual interseismic loading from the

adjacent subduction zones.

(2) Local-and-transient mode (scales around an

open circle in Fig. 10). The remaining part of

the anomalies occurred only for brief moments,

from several months to a few years, and affected

zones from 70 to a few hundred kilometers

wide. For example, there were two notable cases

where the transient shifts in areal contractional

and shear strain rates were remarkably synchro-

nous with the sequences of nearby major

tectonic episodes including both large earth-

quakes and slow events (Figs. 7a and b;

Sections 3.1 and 3.2).

In Shikoku and Kinki regions, the areal contrac-

tional strain rates had weakened suddenly at the turn

of the century, when the W. Tottori and Geiyo

earthquakes occurred (Figs. 7a and 8). The Tokai

slow event (Ozawa et al., 2002) (or aseismic slip on

the subduction fault) was also happening some 500

km away east of the W. Tottori epicenter. All of these

events would cause the stresses in the upper plate

areas to decrease.

In order to determine the stress changes caused by

transient aseismic slips on a subduction fault, it is

essential to have precise knowledge of the spatial

extent, magnitude, and duration of the slips. However,

it is quite difficult to estimate these items solely from

an observation of crustal surface deformation. The

most useful vertical component of strain has the

poorest resolution with GPS observations (e.g.,

Melbourne and Webb, 2003).

Optionally, there is a possibility that transient rate

changes in microseismicity (MN=3) on the subduction

fault (a lower right graph, Fig. 11) might help

determine the precise duration and extent of the

Inland Seismicity

Subduction Slab Seismicity

4

6

4

6M

M

048

12x 10

20

Cum

ulat

ive

en

ergy

rel

ease

7 x 10(mainshock)

21

1930

R=25km

R=150km

Quiescence

1940 1950 1960 1970 1980 1990 2000

R=25km

Inland Seismicity before W.Tottori Earthquake (Depth < 25km)

1998 1999 2000 2001 20020

0.2

0.4

0.6

0.8

1

Time [year]

Cum

ulat

ive

num

ber

(nor

mal

ised

)

Subduction Slab Seismicity (M>3)

WT (inland)

GY (intra-slab)

Zone E

Zone W

130 132 134 136 13831

32

3334

35

36

R=25km R=150km

Zone E (N=964)

Zone W (N=1420)

GY (Depth=51.4km)

WT (Depth=11.3km)

Fig. 11. Seismicity rate changes around the turn of the century in southwestern Japan. (1) Inland seismicity before the 2000 W. Tottori

Earthquake, within 25 km of the epicenter (top), and within 150 km of the epicenter (bottom). (2) Subduction slab seismicity. WT=W. Tottori

earthquake. GY=Geiyo earthquake. The microseismicity rate in Zone E changed at 2000 (increased out of the background level), at dWTT(further rate increase, indicative of a triggered aseismic slip), and at 2001 (decreased back to the background level). The earthquake catalogue of

the Japan Meteorological Agency and their affiliates (2003) used here was generally dhomogeneous (Habermann, 1983)T and dcomplete (e.g.,Wiemer and Zuniga, 1994)T.


aseismic slip in combination with geodetic observa-

tions. A separate detailed study on this subject is

necessary. (It would also be interesting to investigate

the relationship between the non-volcanic tremors

(Obara, 2002) and slow events, as was done in the

Cascadia subduction zone (Rogers and Dragert,

2003).) Since the shear stress changes on the fault

would likely be reflected as changes in the micro-

seismicity rate, it is plausible that the plate coupling

strengths on the Tokai to Tonankai (and possibly a

part of Nankai) subduction faults had weakened

slightly during 2000 to 2001, followed by the Geiyo

earthquake in 2001 (Fig. 11). Particularly, the flow of

these tectonic events appeared in sync with the

decrease of areal contractional strain rates on the

overriding plate regions (Figs. 7a and 8). It is

conceivable that the scale of crustal deformation and

seismicity would correlate well only when their

operative scales match.

The situation in Miyagi Prefecture was similar to

the case in southwestern Japan insofar as the areal

contractional and shear strain rates were higher in the

overriding plate before the recent sequence of large

earthquakes (both inland and offshore events). The

tectonic setting in northeastern Japan is overall differ-

ent from that of southwestern Japan. The overriding

plate in northeastern Japan is under trench-normal

compression and the rate of subduction is much faster

(and the slab is colder) than that of southwestern Japan

(Wang and Suyehiro, 1999). Accordingly, the earth-

quake production rate in northeastern Japan is much

faster than that of the southwest, for example.

The strain is evidently being accumulated near

Miyagi Prefecture. The Headquarters for Earthquake

ID 950392

ID 950393

WT

Station ID: 950393; on WGS84 (annual and semi-annual additive seasonality and linear trend removed)

0 400 800 1200 1600

NS(cm)

Time (days)

-1

0

1 WT

Fig. 12. Small precursory displacements detected at a few GEONET

stations (e.g., station d950393T) near the 2000 W. Tottori earthquakeepicenter (dWTT). Station position time series at the station d950393T(North–South component) on the WGS84 reference ellipsoid is

shown. Data are for 1998/7/18–2002/12/25. Signals at the station

d950392T were also very similar to those at the station d950393T.dWTT=W. Tottori earthquake.


Research Promotion in Japan (ERP at http://

www.jishin.go.jp) gave their forecast for the next

M7.5-class interplate Miyagi-Oki earthquake to

occur in the next 30 years at the probability of

90% or greater, as estimated from earthquake

recurrence-time studies.

Wang (1995), for example, viewed that strain

accumulation at a subduction zone might take place

on multiple spatial scales. Elastic strain energy

induced by distant tectonic forces is stored up in a

broad region in the lithosphere, while the strain is also

accumulated locally around isolated asperities on a

subduction fault. Locally accumulated strain is even-

tually released as earthquakes near asperities. Because

fast crustal shortening (inelastic permanent deforma-

tion) in the overriding plate is typically not observed,

the remaining stored strain energy must be released by

some other effective mechanism(s) conceivably on the

subduction fault (Wang, 1995). With the knowledge

of prevalent low seismic coupling factors at world-

wide subduction zones, compiled by Pacheco et al.

(1993), Wang (1995) suggested that aseismic slip

must be the predominant mechanism of strain releases

at a subduction zone, where the growth of a single

seismic slip with a rapid elastic rebound of the

overriding plate is hindered by the viscous force in

the asthenosphere. Although the viscoelasticity of the

asthenosphere may not be the sole factor in control-

ling the low seismic coupling factors at world’s

subduction zones (Hirahara, 2002), our observations

are not in conflict with Wang (1995)’s observations of

a common subduction zone environment where

aseismic slips are prevalent and multiscale strain

accumulation zones exist. If each pair of rotational

ATZs along the Pacific (Fig. 7c) is presumed to

constitute a subduction-induced strain accumulation

zone, some of the pairs would make up zones several

hundred kilometers wide. They are clearly larger than

a single historic interplate earthquake rupture in the

area. The prevalence of aseismic slips and the

existence of nested strain accumulation zones seem

to be in accord with our findings.

4.3. Limitations of the scheme

Our ATZ-mapping tool successfully delineated

sharp mesoscale tectonic boundaries; however,

dmicroscaleT features were outside our perceivable

range of scale (Fig. 10). Therefore, we were unable to

deduce the style of microscale deformations, e.g.,

along a rotational ATZ, whether they involved multi-

ple distinct block rotations or more diffused deforma-

tions within a zone of concentrated deformation. Also,

most precursory deformations of an inland earthquake

(if there were any tangible ones) on an imminent

rupture surface,

Robust and exploratory analysis of active mesoscale tectonic zones in Japan...

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